A rational number has a decimal expansion which is eventually periodic, that is from some point on there is a string of digits of some length that is just repeated continually.

That the given number does not have that property just consider how far to the right the digit strings: 10, 100, 1000, 10000, ... first appear. What this shows is that for any given N the expansion has not become periodic before reaching N digits (since one of these strings first appears to the right of the N'th digit. Hence it does not become periodic period.